parameteruncertainty

Parameter uncertainty refers to the lack of precise knowledge about the value of a model parameter. In frequentist statistics, a parameter is considered fixed but unknown, and the data are random, so sampling variability induces uncertainty about the parameter’s true value. In Bayesian analysis, parameters are treated as random variables with a prior distribution updated to a posterior distribution by the data, which directly expresses uncertainty about the parameter.

Sources of parameter uncertainty include finite sample sizes, measurement error, and model misspecification. Additional factors are omitted variables, data processing choices, and, in Bayesian contexts, uncertainty in the prior. The combination of these elements determines the width of the uncertainty interval around the parameter estimate and affects the reliability of inferences.

Quantification and communication of parameter uncertainty employ different frameworks. Frequentist methods use standard errors and confidence intervals, often derived from asymptotic theory or resampling techniques such as bootstrapping. Bayesian methods express uncertainty with posterior distributions and credible intervals, incorporating prior information and the model structure. Sensitivity analysis and identifiability checks help assess robustness of conclusions to changes in parameter assumptions.

The implications of parameter uncertainty extend to predictions and decisions. Higher uncertainty about parameters leads to wider predictive intervals and more cautious conclusions. Uncertainty can be reduced by collecting more data, improving measurement quality, or adopting models that yield more identifiable parameters, though it may never be eliminated entirely.

See also: parameter identifiability, measurement error, model uncertainty, predictive uncertainty, confidence interval, credible interval, Fisher information, bootstrapping.